Author

Heng Ma

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Preprint Sep 2026

Extremal separation times and clade-count dynamics in fragmentation trees: a freezing transition

Motivated by the continuous-time critical beta-splitting tree, we investigate chronological trees recording the successive block splits and their times in homogeneous fragmentation processes restricted to $n$ labels. The separation time of a subset is the first time its labels cease to lie in a common block. For each f...

Heng Ma · 1 citation

Preprint Sep 2026

The height of discrete-time critical beta-splitting trees

We determine the asymptotic height of the discrete-time critical beta-splitting tree. Let $L_n^*$ denotes the height of the tree with $n$ leaves, defined as the maximum graph distance from the root to a leaf. Then, \[ \frac{L_n^*}{(\log n)^2} \longrightarrow C_{\mathrm{ht}}:=\min_{\theta>1} \frac{\theta}{2\{\psi(\theta...

Heng Ma · 1 citation

Preprint Aug 2026

Aging in a spin glass with logarithmic correlations

We consider a continuous-time random walk on the discrete two dimensional box, driven by the discrete Gaussian Free Field (DGFF) acting as potential: When at a vertex, the walk waits an exponentially distributed time with mean given by the exponential of the field times an inverse temperature parameter and then jumps t...

A. Cortines, O. Louidor, Heng Ma et al. · 0 citations